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Auralith Learning

Year 8 · Maths · Sequences and the nth term · Lesson 3

Using the nth term

Use the nth term to decide whether a number is in a sequence, find which term has a given value, and find the first term above or below a value.

Whiteboard video lesson: Using the nth term

31-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Decide whether a number is a term of a sequence
  • Find which term has a given value
  • Find the first term greater than or less than a value
  • Solve problems using the nth term
  • Explain properties of sequences

The method

  1. Make the nth term equal to the number.
  2. Solve to find n.
  3. Whole number: it's a term. Not whole: it isn't.
  4. For 'first term greater than', solve an inequality and round n up.

Key words: nth term, position, term, whole number, inequality.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

The nth term of a sequence is 2n + 5. Which term is equal to 45?

  1. Step 1: 2n + 5 = 45
  2. Step 2: 2n = 40
  3. Step 3: n = 40 ÷ 2 = 20
  4. Step 4: Check: 2 × 20 + 5 = 45

Answer: The 20th term

Question 2

The nth term of a sequence is 4n − 1. Which term is equal to 79?

  1. Step 1: 4n − 1 = 79
  2. Step 2: 4n = 80
  3. Step 3: n = 80 ÷ 4 = 20
  4. Step 4: Check: 4 × 20 − 1 = 79

Answer: The 20th term

Question 3

The nth term of a sequence is 7n + 3. Which term is equal to 73?

  1. Step 1: 7n + 3 = 73
  2. Step 2: 7n = 70
  3. Step 3: n = 70 ÷ 7 = 10
  4. Step 4: Check: 7 × 10 + 3 = 73

Answer: The 10th term